Question 4. Suppose for i=1,...,n both the mean and variance are unknown. Based on n=100 sample data, we would like to test vs a) at a type 1 error level , find a sample statistic T and the rejection region R that correctly controls exactly, i.e., find T and R that satisfy (must be exact in distribution not approximate). b) Compute the asymptotic power of T, i.e., what does converge to as sample size goes to infinity? Question 5. Following question 4, except that the test now becomes vs a) does your previous statistic T still control the type 1 error level correctly for the new hypothesis? Namely, is it true that ? b)Compute the asymptotic power of T in this case r, Ni.d Normal(μι, σι) o : μ1-0.5 HA : μ| < 0.5 We were unable to transcribe this imageWe were unable to transcribe this imageProb(T(X) > RI,11-05) < We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image r, Ni.d Normal(μι, σι) o : μ1-0.5 HA : μ| RI,11-05)